It has been claimed that Lyapunov exponents computed from electroencephalogram or electrocorticogram (ECoG) time series are useful for early prediction of epileptic seizures. We show, by utilizing a paradigmatic chaotic system, that there are two major obstacles that can fundamentally hinder the predictive power of Lyapunov exponents computed from time series: finite-time statistical fluctuations and noise. A case study with an ECoG signal recorded from a patient with epilepsy is presented.